SARIMA Model Forecasting of Short-Term Electrical Load Data Augmented by Fast Fourier Transform Seasonality Detection

Abstract

In this study, Seasonal Autoregressive Integrated Moving Average (SARIMA) model is used to forecast short term electric load data. It is known that electrical load data is affected by weather conditions, therefore the electrical load data will have a seasonal component. For this reason, representing this data in the frequency spectrum domain will reflect the exact seasonal time. As such, Fast Fourier Transformation algorithm (FFT) has been used to detect the existence of the seasonal component in the time series of hourly electrical load data. The FFT technique gives a clear view of the behavior of the time series, which shows the three main components located at frequencies ${f}_{1}=$ 3.17${e}^{-8} {\lt p\gt \lt p\gt H} {z}$, ${f}_{2} =$ 1.157${e}^{-5} {\lt p\gt H} {z}, and {f}_{3} =$ 2.315${e}^{-5} {\lt p\gt H} {z}$. The component that is located at ${f}_{2} =$ 1.157${e}^{-5}$ Hz has a significant amplitude and tends to repeat itself every 24 hours. The model that has been selected to forecast one week ahead of the electrical load data is SARIMA (6,1,1) (4,1,1). Most of the predicted values fall into the 95% of confidence interval. The P-values for Ljung-Box statistic indicate that of P-values are higher than 5%. Unlike other techniques, FFT technique offers a quick view of the data behavior with high accuracy.